PHd in Statistics from Idaho
Homework Due on Friday, and will be graded over the weekend.
Starting with Chapter 5.
Class notes are in Canvas
CDF for two random variables have 3 properties
smallest value is 0
largest value is 1
always non-decreasing
Joint PMF for discrete variables uses summation and has two properties
all probability are between 0 and 1
total probability must be 1
Two way tables, because there are two ways to read it
also known as pivot table and contingency table
make sure you can write and understand in different ways
“O otherwise” must be included for a complete distribution function.
Review Homework will be Homework 1 and due Friday 14th
Properties :
smallest value is 0
total volume under the joint pdf is 1
Notes :
If the limits are given without equal sign then you can apply integral in the same way.
The support is the area on the graph.
Upper limit is only important for PMF of discrete random variables
pdf : \(f_{Y_1,Y_2}\geq0\)
PMF : \(0\leq p(y_1,y_2)\leq 1\)
CDF : \(F(y_1,y_2)=P(Y_1\leq y_1, Y_2\leq y_2)=\int_{-\infty}^{y_2}\int_{-\infty}^{y_1}f(y_1,y_2)dt_1dt_2\)
when we do problems we do not need to write every step of the integral
pay attention to the limits on the double integral (\(y_1\) is on the inner integral, meaning it is integrated first (\(dt_1\) inside \(dt_2\)))
final answer will be a function, not a limit
lowest value must be 0, and highest value must be 1
when you find the cdf you must use \(dt_1\) and \(dt_2\), but don’t need it to use or solve for probabilities
joint pmf (p) : between 0 and 1
joint pdf (f) : nonnegative
Discrete uses summation
MIDTERM